Permeability is an important parameter in the analysis of oil and gas reservoirs. Engineers need an accurate estimate of formation permeability in order to optimize the value of oil and gas reservoirs. The need for permeability data is acute in reservoirs with layers having different permeabilities. However, obtaining an accurate estimate of permeability in layered reservoirs has been always problematic for the following reasons.
First, the traditional methods of estimating permeability are based on either coring, log-core correlations or special well tests that require flowing the well and simultaneously measuring downhole rate and pressure. All of these methods are very expensive and normally require days to weeks for complete analysis. Good log-core correlations often require expensive special tests on cores from several wells. Methods based on less expensive side wall cores are notoriously inaccurate in low to moderate permeability formations.
Another method of measuring permeability is to perform time lapsed induction logging runs wherein mud filtrate invasion is monitored by repeated induction logging runs. This procedure is obviously costly in terms of rig time and logging costs.
The present invention is directed at an improved method for calculating formation permeability which does not require the retrieval of core samples or the performance of time lapsed logging runs. The present invention combines a mud cake build-up/invasion simulator or model with a fully implicit near-well bore/reservoir simulator or model, with which radial formation resistivities can be computed and compared with log-observed values. The estimated permeability is varied until a match between the computed radial formation resistivities and the log-observed values is achieved. The present invention specifically takes advantages of the new generation of multi-array induction tools which record five or more resistivity values as opposed to the traditional three resistivity values (i.e., the "short guard" or shallow measurement, the medium measurement and the "deep" measurement). The new generation of multi-array induction tools provides five resistivity measurements which will hereinafter be referred to R.sub.1, R.sub.2, R.sub.3, R.sub.4 and R.sub.5 whereby R.sub.1 is the shallow resistivity measurement, R.sub.5 is the deepest resistivity measurement and R.sub.2, R.sub.3 and R.sub.4 are radially spaced medium measurements disposed between R.sub.1 and R.sub.5. R.sub.1 through R.sub.5 all represent average resistivity (or conductivity) values throughout a radial zone. One multi-array induction log tool in current use is the Schumberger AIT.TM. log. It is also anticipated that competing logging companies will be introducing multi-array induction logging tools in the near future.
The invention is an improved method of calculating formation permeability using drilling parameters, drilling fluid, multi-array induction log data and sophisticated forward modeling techniques.
In summary, the time at which a zone of interest is penetrated by the drill bit is recorded. Subsequently, at appropriate time intervals up until the time of logging, the drilling parameters including the depth, bit size, mud circulation rate, outside diameter of the drill pipe, outside diameter of the collars and penetration rate of the drill string are recorded.
Once the zone of interest is penetrated, the drilling parameters are recorded and a mud sample is received downstream from the shale shaker. All changes in the drilling fluid or drilling mud are also recorded until the zone of interest is logged. New mud samples are retrieved in the event the drilling mud is changed. The time at which the multi-array induction log is run is also recorded along with the resistivity values. At least one porosity log is run with the induction log.
The filtration characteristics of the drilling fluid must be determined for input to the permeability estimation procedure. One preferred method of obtaining these characteristics is by conducting a test on the mud similar to that described by Dewan and Chenevert in a paper entitled "Mud Cake Buildup and Invasion in Low Permeability Formations; Application to Permeability Determination by Measurement While Drilling" (paper NN) which was presented at the SPWLA 34th Annual Logging Symposium, Jun. 13-16, 1993. The formation pressure may, be estimated from local knowledge, from an adjacent well, from a drill-stem test or a down-hole testing tool.
A petrophysical evaluation of all available log data is performed to estimate porosity, water saturation, water resistivity, cementation factor, formation temperature, cementation exponent, saturation exponent, shale volume, shale resistivity, capillary entrance pressure, irreducible water saturation, pore geometry exponent, residual gas saturation and other log-derived parameters and properties. The petrophysical evaluation is carried out by techniques known in the art and described below. The water saturation equation that is used in the petrophysical evaluation, such as Archie, Simandoux or dual-water, must also be used in the permeability analysis algorithm to ensure a consistent analysis.
In the petrophysical evaluation, the filtration equations of Dewan and Chenevert or other suitable filtration equations, the two phase immiscible fluid displacement equations for porous media and the dispersion equations for filtrate and formation water salinity distribution are simultaneously solved from the time the zone was penetrated until the time the multi-array induction logs were run. A radial distribution of water saturation and salinity around the bore hole at the time of logging is estimated and a radial resistivity distribution around the bore hole at the time of logging is calculated.
The calculated formation resistivity is used, along with the response function of each multi-array induction log, to calculate the values of resistivity that the logs would show under the computed (or "calculated") conditions. These calculated or synthetic logs are then compared to the measured logs.
Using methods of parameter estimation as set forth below in accordance with the present invention, the values of various model input parameters used in generating the calculated or synthetic logs (including permeability) are varied until the best possible statistical match of the measured log data and the calculated log data is obtained. The permeability of the free hydrocarbon phase (or free water phase in the case of a water-only zone) is thus estimated.
It is therefore an object to the present invention to provide an improved method for estimating permeability based on the use of the new generation multi-array induction logs.
Yet, another object to the present invention is to provide an improved method of estimating formation permeability without obtaining core samples.
Yet another object of the present invention is to provide an improved method of estimating formation permeability without using "time-lapse" induction logging runs.
Still another object to the present invention is provide an improved computer software program for calculating formation permeability based upon the use of a multi-array induction log, a porosity log, drilling and drilling fluid parameters and automatic parameter estimation.